Question

An empty Erlenmeyer flask weighs 241.3 g. When filled with water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right),\) the flask and its contents weigh \(489.1 \mathrm{~g} .\) (a) What is the volume of water in the flask? (b) How much does the flask weigh when filled with the same volume of chloroform \(\left(d=1.48 \mathrm{~g} / \mathrm{cm}^{3}\right) ?\)

Short answer

Volume of water is 247.8 cm³. Total weight of flask with chloroform is 608.044 g.

Step-by-step solution

- Determine the Mass of Water

First, find the mass of the water by subtracting the weight of the empty flask from the total weight when filled with water.\[ m_{\text{water}} = 489.1 \text{ g} - 241.3 \text{ g} = 247.8 \text{ g} \]

- Calculate the Volume of Water

Next, use the density of water to find the volume of water. The density formula is \( d = \frac{m}{V} \), where \( d \) is the density, \( m \) is the mass, and \( V \) is the volume. Rearrange to solve for volume, \( V = \frac{m}{d} \).\[ V_{\text{water}} = \frac{247.8 \text{ g}}{1.00 \text{ g/cm}^3} = 247.8 \text{ cm}^3 \]

- Calculate Mass of Chloroform

Using the same volume of chloroform, find the mass by multiplying the volume by the density of chloroform.\( m_{\text{chloroform}} = d \times V \).\[ m_{\text{chloroform}} = 1.48 \text{ g/cm}^3 \times 247.8 \text{ cm}^3 = 366.744 \text{ g} \]

- Determine the Total Weight of the Flask with Chloroform

Finally, add the mass of chloroform to the weight of the empty flask.\[ m_{\text{total}} = 241.3 \text{ g} + 366.744 \text{ g} = 608.044 \text{ g} \]

Key concepts

Understanding Mass

Mass is a measure of the amount of matter in an object. It is commonly measured in grams (g) or kilograms (kg). In our exercise, the mass of the empty Erlenmeyer flask is initially given as 241.3 g. When filled with water, the flask’s mass increases to 489.1 g. To find the mass of the water alone, we simply subtract the mass of the empty flask from the filled flask. This makes it clear that:
\[ m_{\text{water}} = 489.1 \text{ g} - 241.3 \text{ g} = 247.8 \text{ g} \]
Understanding how to calculate mass helps us determine how much of a substance is present.

Measuring Volume

Volume measures the space that a substance occupies and is typically measured in cubic centimeters (\text{cm}^3) or liters (L). In the exercise, we need to find the volume of water using its mass and density. Density (\text{d}) is the mass of a substance per unit volume and is commonly given in \text{g/cm}^3. The formula that relates mass, volume, and density is:
\[ d = \frac{m}{V} \]
To find the volume, we rearrange the formula to:
\[ V = \frac{m}{d} \]
Given the mass of water (247.8 g) and its density (1.00 \text{g/cm}^3), the calculation is:
\[ V_{\text{water}} = \frac{247.8 \text{ g}}{1.00 \text{ g/cm}^3} = 247.8 \text{ cm}^3 \]
This simple calculation helps us determine that the volume of the water in the flask is 247.8 \text{cm}^3.

Calculating Density

Density is a crucial concept that connects mass and volume. It tells us how tightly matter is packed in a substance. The formula for density is:
\[ d = \frac{m}{V} \]
For chloroform, we use the same volume as the water but with a different density. The density of chloroform is 1.48 \text{g/cm}^3. To find the mass of chloroform, we multiply the volume by the density:
\[ m_{\text{chloroform}} = d \times V = 1.48 \text{ g/cm}^3 \times 247.8 \text{ cm}^3 = 366.744 \text{ g} \]
Lastly, to find the total weight of the flask when filled with chloroform, we add the mass of the chloroform to the mass of the empty flask:
\[ m_{\text{total}} = 241.3 \text{ g} + 366.744 \text{ g} = 608.044 \text{ g} \]
Understanding how to calculate density, mass, and volume helps us solve real-world problems like this one with ease.